please help i have a test tmw

Given:

The function is:

[tex]f(x)=-(x+5)(x+1)[/tex]

To find:

The range of the function.

Solution:

We have,

[tex]f(x)=-(x+5)(x+1)[/tex]

It can be written as:

[tex]f(x)=-(x^2+x+5x+5)[/tex]

[tex]f(x)=-(x^2+6x+5)[/tex]

Add and subtract square of half of coefficient of x, i.e., [tex]\left(\dfrac{6}{2}\right)^2=9[/tex].

[tex]f(x)=-(x^2+6x+9-9+5)[/tex]

[tex]f(x)=-(x^2+2(x)(3)+3^2-4)[/tex]

[tex]f(x)=-(x^2+2(x)(3)+3^2)+4[/tex]

[tex]f(x)=-(x+3)^2+4[/tex]

On comparing this equation with [tex]f(x)=a(x-h)^2+k[/tex], we get

[tex]a=-1[/tex], it means the graph of the function is a downward parabola and the vertex is the point of maxima.

[tex]h=-3[/tex]

[tex]k=4[/tex]

The vertex of the function is (-3,4). So, the value of the function cannot be greater than 4.

Therefore, the range of the function is all real numbers less than or equal to 4.

Note: All options are incorrect.

11 is the mystery number

Answer:

The mystery number is 11

Step-by-step explanation:

→ Set up an equation

( 10 + 4 + 7 + x ) ÷ 4 = 8

→ Multiply both sides by 4

21 + x = 32

→ Minus 21 from both sides

x = 11

Answer:

42 and 43.

Step-by-step explanation:

This problem can be solved just by knowing the sum of the page numbers, as page numbers on the same face are always one digit apart. Thus we can take 85, subtract 1, divide by 2, and then get 42,42, and add 1 back to the second-page number.

To check our work we can multiply 42*43 to get 1806.

Step-by-step explanation:

here's the answer to your question

Answer:

The answer is Angle 4 and Angle 3.

Answer:

It's answer is angle 4 and angle 3

Answer:

94º

Step-by-step explanation:

<TRS = 1/2(arc UJ + arc TS)

<TRS = 1/2(65 + 123)

<TRS = 1/2(188)

<TRS = 94º

Answer:

x = 240

Step-by-step explanation:

Using the Altitude- on- Hypotenuse theorem

(leg of large triangle)² = ( part of hypotenuse below it) × (whole hypotenuse)

x² = 144 × 400 = 57600 ( take the square root of both sides )

x = [tex]\sqrt{57600}[/tex] = 240

x = 240

Using Pythagoras' theorem on the 3 triangles of sides (as shown in the graphic - the 2 smaller inner triangles and the large main triangle) it can be shown that the height is the square root of the product of both segments of the baseline.

let's call the 2 segments p and q.

p+q = 400

p = 144

q = 400 - 144 = 256

so, as said before, height = sqrt(p×q) = sqrt(144×256) = 192

now the main Pythagoras with the smallest triangle to get x

x² = 192² + 144² = 36864 + 20736 = 57600

x = 240

now, FYI, why is that formula true ?

as we said, we called the segments of the long baseline p and q.

then we can the sides of the main triangle x and y.

and the height is simply h.

so, then we have for the main rectangular triangle

(p+q)² = x² + y²

and for the 2 smaller triangles

x² = p² + h²

y² = q² + h²

=>

p² +2pq + q² = p² + h² + q² + h²

2pq = 2h²

h² = pq

h = sqrt(pq)

and there you have it. just as simple as that.

Answer:

V(t) = 14,000(0.89)^t

Step-by-step explanation:

Present value of the Dodge Challenger = $14,000

Present percentage value = 100%

Depreciation value = 11%

Number of years = t

Future value = V(t)

V(t) = Present value of the Dodge Challenger(Present percentage value - Depreciation value)^t

= 14,000(100% - 11%)^t

= 14,000(89%)^t

= 14,000(0.89)^t

V(t) = 14,000(0.89)^t

Answer:

308.2

Step-by-step explanation:

= 308.2

Answer:

The vertex is (2,1)

Step-by-step explanation:

ƒ(x) = –x^2 + 4x – 3

Factor out the negative

   = -(x^2 -4x+3)

 Factor

What 2 numbers multiply to +3 and add to -4

-3*-1 = 3

-3+-1 = -4

f(x) =  -( x-3)(x-1)

Find the zeros

0 = -( x-3)(x-1)

0 = x-3   0 = x-1

x=3            x=1

The x value of the vertex is 1/2 way between the two zeros

(3+1)/2 = 4/2 =2

To find the y value, substitute x=2 in

f(2) =  -( 2-3)(2-1)

       =-(-1)(1) = 1

The vertex is (2,1)

Answer:

11

Step-by-step explanation:

To calculate the mean you add all the numbers and divide by the number of numbers. There are 4 numbers in this set so we will divide by 4.

Let x be the unknown number,

(10+4+7+x)/4=8(mean)

To solve for x, we first mutliply both sides by 4.

To simplify the left side we can add 10+4+7 and get 21 where now our equation is 21+x=32. Subtract 21 on both sides and you will get 11 which is our answer.

Plug-in 11 and solve for the mean to verify where we do indeed get 8 as the mean.

Answer:

3.1°

Step-by-step explanation:

Given the temperature values :

12 degrees, -2 degrees, -6 degrees, and 8.4 degrees

To obtain the average temperature, take the sum of the temperatures and divide by the number of days

Sum of temperature values : (12 + (-2) + (-6) + 8.4) = 12.4 degree

Sum of temperature / 4

= 12.4 / 4

Average temperature = 3.1 degrees

Answer:

[tex]-10+i\sqrt{2}[/tex]

Step-by-step explanation:

One is given the following expression:

[tex]\sqrt{4}-\sqrt{-98}-\sqrt{144}+\sqrt{-128}[/tex]

In order to simplify and solve this problem, one must keep the following points in mind: the square root function ([tex]\sqrt{}[/tex]) is a way of requesting one to find what number times itself equals the number underneath the radical sign. One must also remember the function of taking the square root of a negative number. Remember the following property: ([tex]\sqrt{-1}=i[/tex]). Simplify the given equation. Factor each of the terms and rewrite the equation. Use the square root property to simplify the radicals and perform operations between them.

[tex]\sqrt{4}-\sqrt{-98}-\sqrt{144}+\sqrt{-128}[/tex]

[tex]\sqrt{2*2}-\sqrt{-1*2*7*7}-\sqrt{12*12}+\sqrt{-1*2*8*8}[/tex]

Take factors from out of under the radical:

[tex]\sqrt{2*2}-\sqrt{-1*2*7*7}-\sqrt{12*12}+\sqrt{-1*2*8*8}[/tex]

[tex]2-7i\sqrt{2}-12+8i\sqrt{2}[/tex]

Simplify,

[tex]-10+i\sqrt{2}[/tex]

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Answer:

900 is the correct awnser

Answer:

6÷3

=2

So each chimpanzee Will get 2 bananas

Answer:

its letter c so 80

Step-by-step explanation:

I hope this help

Step-by-step explanation:

a+b+c=78

b=10+a

c=2b

then, we back the first

a+10+a+2b=78

2a+2b=78- 10

2a+2(10+a)=68

2a+2a=48

4a=48

a=12

b=22

c=44

Answer:

This type of study is called a simulation

Step-by-step explanation:

Answer:

1365 rupees

Step-by-step explanation:

1. Approach

The easiest method to solve this problem is via the method of proportions. One can use a proportion to find the original price of the watch. Then one can find the price of the watch if the watch had a (30%) mark up, by using a proportion.

2. Find the original price

Remember, the general format of a proportion is the following:

[tex]\frac{part}{total}=\frac{percent}{100}[/tex]

The following information is given:

The watch sold for (1260) rupees which is (120%) of the original price. Remember, there was a (20%) gain, meaning that the seller recovered (120%) of the price, in essence, the price of the watch, plus (20%) extra, thus (120%). Substitute these values into the proportion and solve,

[tex]\frac{part}{total}=\frac{percent}{100}[/tex]

[tex]\frac{1260}{total}=\frac{120}{100}[/tex]

Simplify,

[tex]\frac{1260}{total}=\frac{120}{100}[/tex]

[tex]\frac{1260}{total}=\frac{6}{5}[/tex]

Cross product,

[tex]\frac{1260}{total}=\frac{6}{5}[/tex]

[tex](5)(1260)=(6)(total)[/tex]

Simplify,

[tex](5)(1260)=(6)(total)[/tex]

[tex]6300=6*total[/tex]

Inverse operations,

[tex]6300=6*total[/tex]

[tex]1050=total[/tex]

3. Find the price if the mark up is (30%)

Now, one knows the original price of the watch. Set up a proportion to find the price of the watch if there is a (30%) mark up. Use the same logic to set up this proportion as was used to set up the last one. The (percent) will be (130%) because the new price of the watch is (130%) of the original watch.

[tex]\frac{part}{total}=\frac{percent}{100}[/tex]

Substitute,

[tex]\frac{part}{total}=\frac{percent}{100}[/tex]

[tex]\frac{part}{1050}=\frac{130}{100}[/tex]

Simplify,

[tex]\frac{part}{1050}=\frac{130}{100}[/tex]

[tex]\frac{part}{1050}=\frac{13}{10}[/tex]

Cross products,

[tex]\frac{part}{1050}=\frac{13}{10}[/tex]

[tex](10)(part)=(13)(1050)[/tex]

Simplify,

[tex](10)(part)=(13)(1050)[/tex]

[tex]10*part=13650[/tex]

Inverse operations,

[tex]10*part=13650[/tex]

[tex]part=1365[/tex]

Thus, the price after the (30%) is (1365) rupees.

Answer:

[tex]2^{\frac{1}{6} }[/tex]

Step-by-step explanation:

(2^1/3)^1/2 = 2^(1/3 x 1/2) =2^1/6

Answer:

She spends $30 in total.

Step-by-step explanation:

Suppose that you buy X units of a given product with a price Y, then the total cost here is X*Y, with this we can solve our problem:

Every week Judy buys:

5 carrots, at $1 each, so she spends 5*$1 = $5 in carrots.

3 bottles of milk at $3, so she spends 3*$3 = $9 in milk bottles.

2 pineapples at $4 each (but the pineapples are at half price, so this week the pineapples cost $4/2 = $2), so she spends 2*$2 = $4 in pineapples.

2 bags of flour at $5 each, so she spends 2*$5 = $10 in flour.

1 giant container of ice cream, she spends $7 on it.

So the total money that she speends is:

$5 + $9 + $4 + $10 + $7 = $35

And she has a coupon for $5 in any order equal to or larger than $25, his order is larger than $25, so she can use the coupon.

So she will spend a total of $35 - $5 = $30

She spends $30 in total.

Answer:

The dilation scale factor is [tex]\frac{1}{2}[/tex].

Step-by-step explanation:

The image is the dilated form of its preimage if and only if the following conditions are observed:

1) [tex]K' = \alpha_{1} \cdot K[/tex]

2) [tex]T' = \alpha_{2} \cdot T[/tex]

3) [tex]P' = \alpha_{3} \cdot P[/tex]

4) [tex]J' = \alpha_{4} \cdot J[/tex]

5) [tex]\alpha_{1} = \alpha_{2} = \alpha_{3} = \alpha_{4}[/tex]

If we know that [tex]K = (2, 0)[/tex], [tex]K' = (1, 0)[/tex], [tex]T = (3, 0)[/tex], [tex]T' = (1.5,0)[/tex], [tex]P = (1, 5)[/tex], [tex]P' = (0.5, 2.5)[/tex], [tex]J = (0, 3)[/tex] and [tex]J' = (0, 1.5)[/tex], then the coefficients are, respectively:

[tex]\alpha_{1} = \frac{1}{2}[/tex], [tex]\alpha_{2} = \frac{1}{2}[/tex], [tex]\alpha_{3} = \frac{1}{2}[/tex], [tex]\alpha_{4} = \frac{1}{2}[/tex]

As [tex]\alpha_{1} = \alpha_{2} = \alpha_{3} = \alpha_{4}[/tex], we conclude that the dilation scale factor applied in the preimage is equal to [tex]\frac{1}{2}[/tex].

Answer:

it is an rigjt angle triangle you shoult pythogores therom if you will know it it will be easy to you to understand this question